What is a Linear Time Invariant (LTI) System?

Explains what a Linear Time Invariant System (LTI) is, and gives a couple of examples.
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By watching your videos i was able to solve all signal systems questions in a very tough Indian engineering competitive exam called GATE.

[@iain_explains]

I'm so glad to hear that the videos have helped. Good luck with the exam.

[@kartheekpattigilli2759]

I can't thank you enough,,, i love your explanation sir ,, thanks from india

[@iain_explains]

I'm so glad you found the video helpful.

[@stringstoparadise2392]

sir, can you comment upon the linearity and nonlinearity of our wireless channel? according to me, the channel would be nonlinear as the channel coefficient is under rayleigh fading which would lead to distortion in phase and amplitude. but my doubt is that than how we are writing the impulse response of the channel rather an impulse response is defined for only LTI systems

[@iain_explains]

Wireless channels are linear. For linear systems, when the input is a sinusoid, the output is a sinusoid at the same frequency. The amplitude and phase will (in general) be different, but there is no change to the frequency. The key point is that amplitude and phase changes are not "distortion".

[@stanleyche470]

@@iain_explains hello professor since the wireless channel is random in nature thus it cannot follow the property of homogeneity as the gain provided by the channel for different inputs at different intervals of time would be not the same but the principle of homogeneity tells us that for the system to be linear the o/p should be scaled by the same factor as that of input

[@Bao_Bab666]

Hello Sir, I set up the following chain : DAC -> LTI System (a filter) -> ADC and my aim is to plot the bode diagram (magnitude/phase) automatically. I was wondering if there a mathematical tools / known-mehod to extract the magnitude and phase information ?

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excellent explanation

[@iain_explains]

Thanks. Glad you liked it!

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[@iain_explains]

Most welcome!

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Very useful , thanks a lot

[@iain_explains]

Glad it was helpful!

[@daopengliu6138]

Hello, sir. Is that y(t) = x(t) times h(t) in your figures ? If so, y(t) = 1 x h(0) in the first figure, how could y(t) be a continuous time figure.

[@iain_explains]

No, that is the symbol for convolution. For more information on convolution, see: "What is Convolution? And Two Examples where it arises." kzbin.info/www/bejne/jmPGe2usdshjg7c

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dr why h being h(t-tow) whats happened

[@iain_explains]

Perhaps this video might help to explain: "Convolution Equation Explained" kzbin.info/www/bejne/iJ7IgXqBjLSGg7M

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[@iain_explains]

I'm glad it was helpful anyway.

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[@iain_explains]

That's great to hear. I'm so glad you're finding the videos useful.

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[@iain_explains]

Thanks for letting me know. It's great to hear these sorts of comments - it motivates me to keep making more videos.

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[@iain_explains]

Great. Glad the videos are helpful.

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Sir Indian Student will love to have teacher like you...! Thank you for the lecture

[@iain_explains]

It's my pleasure. Please tell your friends about the channel too. The more people I can help, the better. Have you seen my website with a full listing of all the videos? iaincollings.com

[@rijass8841]

Thank you.

[@albertdot5704]

Sir I m in confusion please tell Which of following will definitely non lti system here Sint is input and S1 S2 S3 are systems A. Sint ------[S1]------sin(-t) B. Sint-------[S2]-------sin(2t) C. Sint-------[S3]------{sin(t)}^2

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Thanks you ..! Good Explanation

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[@iain_explains]

My pleasure.

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Your explanation is so helpful thank you!!

[@iain_explains]

Glad it was helpful!

[@qwerty_____146]

Thank you man. But please help about resolve a equation TI and TV system with an example. thank you.

[@primaryforest2947]

What is an impulse response

[@iain_explains]

You just need to search my channel! or check my website iaincollings.com and you'll find the answer: "What is an Impulse Response?" kzbin.info/www/bejne/jYXQlp-Ii8SMr9E

[@tomdella9255]

I can't believe it's this simple, my lectures spent an hour on this and I left more confused about what it meant than when I started thir lecture. Having got your explaination their lecture now makes waaaaay more sense, but they really should have started with any explaination before diving into the mathematical proofs.

[@iain_explains]

Glad the video was helpful. It's always helpful to have examples and break things down.

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[@iain_explains]

I'm so glad to hear that you like my explanation. Have you seen my other videos on the channel? They're all listed here, in categorised order: iaincollings.com

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Thank you very much 🙏🙂 Non linear system rectifier (x(t))^2

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Thanks for the suggestion. I've put it on my "to do" list.

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[@iain_explains]

I'm glad you're finding the videos helpful.

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[@iain_explains]

Thanks.

[@tıbhendese]

4:21 I don't understand that point, x is just an impulse function and y is a different function. Is it really equals to = [some constant] times [x(t)] ?

[@iain_explains]

I'm not sure what you are asking, sorry. At the 4:21 point, I am just giving an example of a functional relationship between x(t) and y(t). It's just one example, in which y(t) simply equals a constant gain, times the input x(t). That is exactly what an amplifier does.

[@tıbhendese]

@@iain_explains thank you for answering, this is the point that I don't understand. Why it's equal to a constant number? Xt, yt, and ht are (generally) completely different functions in systems. How H(t) is equal to a constant gain in t domain? S domain may be understandable a bit, but convolution is also complicated.

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[@iain_explains]

Glad it helped!

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[@iain_explains]

You're most welcome